Is this a correct answer, I'm trying to integrate the marginal revenue function to get the function for total revenue.

R'(x)=(30/(2x +1)^2)+30
=R(x)=(-15/2x+1)+30x

yes, but don't forget to add a constant C

To determine if an answer is correct, we can differentiate the function R(x) and check if it matches the marginal revenue function R'(x) given. If the derivatives match, then the answer is likely correct.

To find the function for total revenue (R(x)), you need to integrate the marginal revenue function (R'(x)).

Starting with the given marginal revenue function:
R'(x) = (30/(2x +1)^2) + 30

To integrate this, we need to find the antiderivative of R'(x).

First, let's integrate the first term:
∫(30/(2x + 1)^2) dx

To solve this integral, we can use the substitution method. Let u = 2x + 1, then du/dx = 2.

Substituting u and du into the integral:
∫ (30/u^2) * (1/2) du
= (1/2) * 30 * ∫ u^(-2) du
= 15 * (u^(-1)) + C
= 15 * (1/(2x + 1)) + C1, where C1 is the constant of integration.

Next, let's integrate the second term:
∫ 30 dx
= 30x + C2, where C2 is another constant of integration.

Now we can combine both results:
R(x) = 15 * (1/(2x + 1)) + 30x + C

However, when checking your answer, R(x) = (-15/2x + 1) + 30x, with (-15/2x + 1) being the first term, it seems like there is a sign error. The correct sign in the first term should be positive, not negative.

So the correct function for total revenue is:
R(x) = 15 * (1/(2x + 1)) + 30x + C

Remember to include the constant of integration (C) when integrating, as it accounts for the unknown constant in the original function.